Maths tutor

In the fig. Find the value of y.

Chapter 1 of Class 10 Maths is typically *"Real Numbers"*. Here are some Multiple Choice Questions (MCQs) and Assertion-Reason questions based on this chapter.

# # # **MCQs:**

1. **The HCF of two numbers is 6 and their LCM is 72. If one number is 24, what is the other number?**
a) 12
b) 18
c) 36
d) 48

**Answer:** b) 18

2. **The decimal expansion of the rational number \(\frac{14587}{1250}\) will terminate after:**
a) 2 decimal places
b) 3 decimal places
c) 4 decimal places
d) 5 decimal places

**Answer:** c) 4 decimal places

3. **Which of the following is an irrational number?**
a) \(\frac{22}{7}\)
b) \(0.333\ldots\)
c) \(\sqrt{2}\)
d) 1.41414141…

**Answer:** c) \(\sqrt{2}\)

4. **If two positive integers \(a\) and \(b\) are expressed as \(a = 2^2 \times 3 \times 5\) and \(b = 2 \times 3^2 \times 7\), then HCF \((a, b)\) is:**
a) 42
b) 30
c) 60
d) 6

**Answer:** d) 6

5. **The least number that is divisible by all the numbers between 1 and 10 (both inclusive) is:**
a) 504
b) 1000
c) 2520
d) 840

**Answer:** c) 2520

---

# # # **Assertion-Reason Questions:**

**Assertion (A):** The sum of a rational and an irrational number is always irrational.
**Reason (R):** Irrational numbers have non-terminating, non-repeating decimal expansions.

a) Both A and R are true, and R is the correct explanation of A.
b) Both A and R are true, but R is not the correct explanation of A.
c) A is true, but R is false.
d) A is false, but R is true.

**Answer:** a) Both A and R are true, and R is the correct explanation of A.

---

**Assertion (A):** Every composite number can be factorized as a product of primes.
**Reason (R):** Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of primes in a unique way (apart from the order of the prime factors).

a) Both A and R are true, and R is the correct explanation of A.
b) Both A and R are true, but R is not the correct explanation of A.
c) A is true, but R is false.
d) A is false, but R is true.

**Answer:** a) Both A and R are true, and R is the correct explanation of A.

---

**Assertion (A):** The LCM of two co-prime numbers is always their product.
**Reason (R):** Co-prime numbers are those that do not have any common factors other than 1.

a) Both A and R are true, and R is the correct explanation of A.
b) Both A and R are true, but R is not the correct explanation of A.
c) A is true, but R is false.
d) A is false, but R is true.

**Answer:** a) Both A and R are true, and R is the correct explanation of A.

---

**Assertion (A):** If \(p\) is a prime number, then \(\sqrt{p}\) is irrational.
**Reason (R):** A number is said to be irrational if it cannot be expressed in the form of \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\).

a) Both A and R are true, and R is the correct explanation of A.
b) Both A and R are true, but R is not the correct explanation of A.
c) A is true, but R is false.
d) A is false, but R is true.

**Answer:** a) Both A and R are true, and R is the correct explanation of A.

These questions will help students get a better understanding of the concepts from Chapter 1 on Real Numbers.

Here is a list of different types of questions for practice from **Chapter 1: Real Numbers** of Class 10 Mathematics. This chapter mainly covers concepts like Euclid’s Division Lemma, the Fundamental Theorem of Arithmetic, and revisiting irrational and rational numbers. Let's divide the questions into different categories for effective practice:

# # # **1. Euclid’s Division Lemma**

- **Basic Questions**:
1. Use Euclid's Division Lemma to find the HCF of 56 and 98.
2. Find the HCF of 135 and 225 using Euclid's division algorithm.

- **Intermediate Questions**:
1. Show that any positive integer is of the form \(3q\), \(3q+1\), or \(3q+2\) for some integer \(q\).
2. Use Euclid’s Division Algorithm to find the largest number which divides 245 and 1029 leaving remainders 5 and 3 respectively.

- **Challenging Questions**:
1. Prove that the product of two consecutive positive integers is divisible by 2.
2. Show that the square of any positive integer is either of the form \(3m\) or \(3m+1\).

---

# # # **2. The Fundamental Theorem of Arithmetic**

- **Basic Questions**:
1. Find the prime factorization of 2310.
2. Using the Fundamental Theorem of Arithmetic, find the LCM and HCF of 18 and 48.

- **Intermediate Questions**:
1. Prove that 7 is irrational.
2. Express 156 as a product of its prime factors.

- **Challenging Questions**:
1. Prove that there are infinitely many prime numbers.
2. Explain why \( \sqrt{5} \) is irrational.

---

# # # **3. Revisiting Irrational Numbers**

- **Basic Questions**:
1. Prove that \( \sqrt{2} \) is irrational.
2. Show that \( 3 + \sqrt{2} \) is irrational.

- **Intermediate Questions**:
1. If \( x = 7 + \sqrt{5} \), prove that \( x \) is an irrational number.
2. Explain why the sum or difference of a rational and an irrational number is always irrational.

- **Challenging Questions**:
1. Prove that \( \sqrt{3} + \sqrt{5} \) is irrational.
2. Prove that if \( a \) is a rational number and \( b \) is an irrational number, then \( a + b \) is irrational.

---

# # # **4. Revisiting Rational Numbers and their Decimal Expansions**

- **Basic Questions**:
1. Show that the decimal expansion of \( \frac{1}{7} \) is non-terminating repeating.
2. Write the decimal expansion of \( \frac{1}{8} \).

- **Intermediate Questions**:
1. Without actually performing the long division, state whether the decimal expansion of \( \frac{7}{8} \) is terminating or non-terminating repeating.
2. Show that the decimal expansion of \( \frac{23}{90} \) is non-terminating repeating.

- **Challenging Questions**:
1. Find whether \( \frac{13}{625} \) has a terminating or non-terminating decimal expansion. If terminating, find the number of decimal places.
2. Express \( 0.33333\ldots \) in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers.

---

# # # **5. Mixed Problems**

- **Basic Questions**:
1. Prove that 3 is a factor of \( 9n^2 - n \) for any integer \( n \).
2. Find the least number which is divisible by 18, 24, and 36.

- **Intermediate Questions**:
1. Prove that the square root of any prime number is irrational.
2. Prove that \( \sqrt{3} \) is irrational using contradiction.

- **Challenging Questions**:
1. Prove that \( 2 + 5\sqrt{3} \) is irrational.
2. Find the HCF of \( 135 \) and \( 225 \) using prime factorization and verify it using Euclid’s Division Lemma.

---

These questions cover all types of problems from basic to challenging to help you gain mastery over the concepts in **Chapter 1: Real Numbers**. Practice them step by step to get comfortable with each topic.

Class 10 science hormones mcq

Here are some **MCQs related to hormones** for Class 10 Science:

1. **Which hormone is known as the 'growth hormone'?**
a) Thyroxine
b) Insulin
c) Growth hormone
d) Adrenaline

**Answer:** c) Growth hormone

2. **Which of the following glands produces insulin?**
a) Thyroid
b) Pituitary
c) Pancreas
d) Adrenal

**Answer:** c) Pancreas

3. **Which hormone regulates the metabolism of carbohydrates, proteins, and fats in the body?**
a) Thyroxine
b) Adrenaline
c) Estrogen
d) Insulin

**Answer:** a) Thyroxine

4. **Deficiency of which hormone causes diabetes?**
a) Thyroxine
b) Insulin
c) Adrenaline
d) Growth hormone

**Answer:** b) Insulin

5. **Which hormone prepares the body for emergency situations, often called the "fight or flight" hormone?**
a) Thyroxine
b) Insulin
c) Adrenaline
d) Progesterone

**Answer:** c) Adrenaline

6. **Which hormone controls the release of energy by the oxidation of glucose in the body?**
a) Adrenaline
b) Thyroxine
c) Insulin
d) Testosterone

**Answer:** b) Thyroxine

7. **Which of the following hormones is responsible for the development of secondary sexual characteristics in males?**
a) Estrogen
b) Progesterone
c) Testosterone
d) Insulin

**Answer:** c) Testosterone

8. **Which hormone is responsible for regulating the water balance in the body?**
a) Adrenaline
b) Growth hormone
c) Vasopressin
d) Thyroxine

**Answer:** c) Vasopressin

9. **The hormone estrogen is produced by which gland?**
a) Adrenal gland
b) Pancreas
c) Ovaries
d) Te**es

**Answer:** c) Ovaries

10. **Which of the following hormones controls calcium levels in the blood?**
a) Parathyroid hormone
b) Insulin
c) Adrenaline
d) Thyroxine

**Answer:** a) Parathyroid hormone

These MCQs will help in understanding the key concepts about hormones from the Class 10 Science syllabus.

Class 10 science plant hormones

Here are some MCQs related to **plant hormones** for Class 10 Science:

1. **Which of the following is a plant hormone responsible for cell elongation?**
a) Cytokinin
b) Ethylene
c) Auxin
d) Abscisic acid

**Answer:** c) Auxin

2. **Which plant hormone is responsible for promoting fruit ripening?**
a) Auxin
b) Cytokinin
c) Gibberellin
d) Ethylene

**Answer:** d) Ethylene

3. **Gibberellins help in:**
a) Flowering
b) Seed germination
c) Leaf fall
d) Fruit ripening

**Answer:** b) Seed germination

4. **Which plant hormone inhibits growth and promotes dormancy?**
a) Cytokinin
b) Gibberellin
c) Abscisic acid
d) Ethylene

**Answer:** c) Abscisic acid

5. **The hormone that promotes cell division in plants is:**
a) Ethylene
b) Cytokinin
c) Auxin
d) Abscisic acid

**Answer:** b) Cytokinin

6. **Which of the following hormones promotes the growth of lateral buds?**
a) Auxin
b) Cytokinin
c) Gibberellin
d) Ethylene

**Answer:** b) Cytokinin

7. **Which plant hormone is also known as the 'stress hormone' because it helps plants to cope with stress conditions like drought?**
a) Ethylene
b) Cytokinin
c) Abscisic acid
d) Auxin

**Answer:** c) Abscisic acid

8. **Which hormone is responsible for bolting in plants, especially in rosette plants?**
a) Auxin
b) Gibberellin
c) Ethylene
d) Cytokinin

**Answer:** b) Gibberellin

9. **What is the primary role of cytokinins in plants?**
a) Root growth
b) Shoot growth
c) Leaf fall
d) Cell division

**Answer:** d) Cell division

10. **Which of the following hormones promotes apical dominance in plants?**
a) Auxin
b) Cytokinin
c) Gibberellin
d) Ethylene

**Answer:** a) Auxin

These MCQs cover key points about plant hormones for Class 10 Science.